Abstract
Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification.
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Acknowledgements
We are grateful to Ben Blumson, Volker Halbach, Carlo Nicolai, and especially Dan Waxman, who gave us great feedback on more than one version of this paper. We would also like to thank two anonymous referees for their valuable objections and suggestions, which helped us improve the paper enormously. This paper was written while Thomas Schindler received support from the European Research Council within the project Truth and Semantics (TRUST, grant agreement no 803684).
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Picollo, L., Schindler, T. Higher-Order Logic and Disquotational Truth. J Philos Logic 51, 879–918 (2022). https://doi.org/10.1007/s10992-022-09654-8
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DOI: https://doi.org/10.1007/s10992-022-09654-8